Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-2, -2), parallel to y=3

Key Concepts

Standard Form of a Linear Equation

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for easily identifying the x- and y-intercepts of the line. To convert from slope-intercept form (y = mx + b) to standard form, you can rearrange the equation to fit the Ax + By = C format.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b is the y-intercept. This form is particularly useful for quickly graphing the line, as it directly provides the slope and where the line crosses the y-axis. Understanding how to manipulate this form is essential for deriving equations based on given points and slopes.

Parallel Lines

Parallel lines are lines in a plane that never intersect and have the same slope. When writing the equation of a line parallel to a given line, it is crucial to use the same slope as the original line. In this case, since the line described is parallel to y = 3, which has a slope of 0, the new line will also have a slope of 0, indicating it is horizontal.